Deep Clear Manga by Miho Obana

Honey Bitter meets Kodomo no Omocha. Shuri is a private detective with a special ability to read minds. She usually handles all sorts of cases, but this time she is faced with a rather unusual request. The famous actress Kurata Sana is going to play in a new film as a detective. She wants to be able to impersonate her character as best as possible so she asks Shuri if she can stick around to learn a few things that real detectives do and how they act. Despite this childish request, Shuri also recieves a more intimate request from Sana's manager, Sagami Rei, who wants to find out the reason why Sana and her husband, Hayama Akito, have decided to live separate one from another.